{
  "annotation_id": "e0b2269d-9809-4d6f-9251-d1c06f5e5798",
  "date_created": "2026-03-02T18:01:38.977000Z",
  "date_modified": "2026-03-02T18:01:38.977000Z",
  "file_hash": "47206ffca662598ba6a1c145de4fa80c60914512af5859524c57eaabc2127146",
  "private": false,
  "record": {
    "abstract": "We find the optimal universal way of manipulating a single qubit,\n|psi(theta,phi)\u003e, such that (theta,phi)-\u003e(theta-k,phi-l). Such optimal\ntransformations fall into two classes. For 0 =\u003c k =\u003c pi/2 the optimal map is\nthe identity and the fidelity varies monotonically from 1 (for k=0) to 1/2 (for\nk=pi/2). For pi/2 =\u003c k =\u003c pi the optimal map is the universal-NOT gate and the\nfidelity varies monotonically from 1/2 (for k=pi/2) to 2/3 (for k=pi). The\nfidelity 2/3 is equal to the fidelity of measurement. It is therefore rather\nsurprising that for some values of k the fidelity is lower than 2/3.",
    "arxiv_id": "quant-ph/0008011",
    "authors": [
      "Lucien Hardy",
      "David D. Song"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.63.032304",
    "journal_ref": "Phys. Rev. A 63, 032304 (2001)",
    "title": "Universal Manipulation of a Single Qubit",
    "url": "https://arxiv.org/abs/quant-ph/0008011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3c21f0ce-8225-44e6-a56f-ecbb25185a7d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}